• Cropping Euler factors of modular L-functions 

    González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles (2013-09)
    Article
    Accés obert
    According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
  • Modular forms with large coefficient fields via congruences 

    Dieulefait, Luis; Jiménez Urroz, Jorge; Ribet, Keneth (Springer, 2015-05-01)
    Article
    Accés obert
    We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. ...
  • On fields of definition of torsion points of elliptic curves with complex multiplication 

    Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (2011-06)
    Article
    Accés obert
    For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...
  • Orders of CM elliptic curves modulo p with at most two primes 

    Iwaniec, H.; Jiménez Urroz, Jorge (2010)
    Article
    Accés restringit per política de l'editorial
    Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the size of the keys involved in the construction and comunication process. About the former one needs a di±cult ...
  • Orders of CM elliptic curves modulo p with at most two primes 

    Iwaniec, Henryk; Jiménez Urroz, Jorge (2006)
    Article
    Accés obert
    We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and considering elliptic curves with complex multiplication. In other words for infinitely many primes $p$, (given in a quantitative ...
  • Small primitive roots and malleability of RSA 

    Jiménez Urroz, Jorge; Dieulefait, Luis Victor (2012)
    Text en actes de congrés
    Accés obert
    In their paper [9], P. Paillier and J. Villar make a conjectur e about the malleability of an RSA modulus. In this paper we present an ex plicit algo- rithm refuting the conjecture. Concretely we can factorize an RSA ...
  • Square-free discriminants of Frobenius rings 

    David, Chantal; Jiménez Urroz, Jorge (2010-09)
    Article
    Accés obert
    Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated ...